Write a polynomial in standard form that is a degree of 3, has zeros - 1, 2i, and P (0) = 8

p (x) = 2 (x³ + x² + 4x + 4)

Step-by-step explanation:

An imaginary root such as 2i must be joined by its complex conjugate, which here is - 2i.

Thus, the zeros are - 1, 2i and - 2i.

The polynomial is p (x) = a (x + 1) (x - 2i) (x + 2i). This is of degree 3.

In expanded form, we have p (x) = a (x + 1) (x² + 4), or

= a (x³ + 4x + x² + 4), or, in standard form,

= a (x³ + x² + 4x + 4).

Since this must equal 8 when x = 0, 8 = a (4). Thus, a = 2.

The polynomial is thus p (x) = 2 (x³ + x² + 4x + 4)